In various fields of engineering, the use of composite materials is widespread. In aerospace structures, for example, composite materials are used to fabricate a variety of curved, non-planar components, such as aerodynamic surfaces, domes, pressurized vessels, and the like. Although desirable results have been achieved using curved composite components, to continue to improve the reliability of such components, it is desirable to provide improved apparatus and methods of tension testing of segments from such curved composite components in such a way that the curved segment do not undergo any undesirable changes in shape due to the tension testing.